A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página vi
... reason geometry is called an ' abstract science . ' A further point to be noticed in regard to the definitions is the relation in which they stand to the whole system of geometry . It has been already remarked that they form the ...
... reason geometry is called an ' abstract science . ' A further point to be noticed in regard to the definitions is the relation in which they stand to the whole system of geometry . It has been already remarked that they form the ...
Página viii
... reason about them and deduce general truths . But this is not the case in regard to straight lines , ' right angles ' and parallel lines . ' Concerning these Euclid enunciates other properties in the 10th , 11th and 12th axioms , and ...
... reason about them and deduce general truths . But this is not the case in regard to straight lines , ' right angles ' and parallel lines . ' Concerning these Euclid enunciates other properties in the 10th , 11th and 12th axioms , and ...
Página 21
... of five circles . The reason of this is also explained on p . 8 . Ex . Show how to produce the less of two lines until it is equal to the greater . PROPOSITION 4. THEOREM . If two triangles have two sides BOOK I. 3 . 21.
... of five circles . The reason of this is also explained on p . 8 . Ex . Show how to produce the less of two lines until it is equal to the greater . PROPOSITION 4. THEOREM . If two triangles have two sides BOOK I. 3 . 21.
Página 30
... reason of which is obvious . Ex . 1. If two isosceles triangles be described on opposite sides of the same base the straight line joining their vertices will bisect their common base at right angles . [ See fig . to the prop . ] 2. If ...
... reason of which is obvious . Ex . 1. If two isosceles triangles be described on opposite sides of the same base the straight line joining their vertices will bisect their common base at right angles . [ See fig . to the prop . ] 2. If ...
Página 43
... reason , the exterior angle CEB of the triangle ABE is greater than the angle BAE ; much more then is the angle BDC greater than the angle BAC . Therefore , if from the ends , & c . Q.E.D. Unless the lines are drawn from " the ends of ...
... reason , the exterior angle CEB of the triangle ABE is greater than the angle BAE ; much more then is the angle BDC greater than the angle BAC . Therefore , if from the ends , & c . Q.E.D. Unless the lines are drawn from " the ends of ...
Otras ediciones - Ver todas
A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... Euclides Vista completa - 1874 |
A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CBA axioms base BC BC is equal bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop PROPOSITION quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal